Methods To Characterize Underground Formation

ABSTRACT

A method for determining a characteristic of an underground formation with a fluid is described. The method includes providing a sample material of the underground formation; measuring the permeability and the porosity of the sample material; performing a drainage test on the sample material using the fluid; estimating the threshold pressure of the sample material from the drainage test, the permeability and the porosity measurements; and determining the receding contact angle of the fluid on the sample material from the threshold pressure. The sample material can be disaggregated material.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to commonly-assigned U.S. patent applicationSer. No. 12/914,463, entitled “Enhancing Hydrocarbon Recovery” and isalso related to commonly-assigned and simultaneously-filed U.S. patentapplication Ser. No. 12/974,116 entitled “Wettability Analysis ofDisaggregated Material”, which is being filed concurrently with thepresent application and incorporated herein by reference in itsentirety.

FIELD

The patent specification is generally related to hydrocarbon recoveryfrom underground formations. More particularly, this patentspecification relates to methods to characterize underground formationsand the effect of treatments on underground material leading to enhancedhydrocarbon recovery from such underground formations.

BACKGROUND

Recovering hydrocarbons such as oil and gas from high permeabilityreservoirs is well understood. However, recovery of hydrocarbonresources from low-permeability reservoirs is more difficult and lesswell understood (See Boyer, C., et al., Producing Gas from Its Source.Oilfield Review, 2006. Autumn 2006: p. 36-49). Consequently, operatorshave until recently tended to bypass low permeability reservoirs such asshales in favor of more conventional reservoirs such as sandstones andcarbonates.

In order to develop methods to efficiently recover gas from anunderground reservoir, it is very useful to gain a good understanding ofthe chemical nature of the formation. For example, a shale reservoirtypically includes a matrix of small pores and may also containnaturally occurring fractures/fissures (natural fractures). Thesenatural fractures are most usually randomly occurring on the overallreservoir scale. The natural fractures can be open (have pore volume)under in-situ reservoir conditions or open but filled in with material(have very little or no pore volume) later in geologic time; forexample, calcite (CaCO₃). These fractures can also be in a closed-state(no pore volume) due to in-situ stress changes over time. Naturalfractures in any or all of these states may exist in the same reservoir.For more complete understanding of the occurrence, properties, behavior,etc. of naturally fractured reservoirs in general, one may review thefollowing references: Nelson, Ronald A., Geologic Analysis of NaturallyFractured Reservoirs (2nd Edition), Elsevier, and Aguilera, Roberto,Naturally Fractured Reservoirs, PennWell Publishing. The permeability ofthe shale pore matrix is typically quite low, e.g., in the less than onemillidarcy range. In a shale gas reservoir, this presents a problembecause the pore matrix contains most of the hydrocarbons. Since the lowpermeability of the pore matrix restricts fluid movement, it would beuseful to understand how to prompt mass transfer of hydrocarbons fromthe pore matrix to the fracture network.

Tight sandstone reservoirs have dominated the hydraulic fracturingmarket in North America for years, and due to their relatively simplelithology (when compared to gas shales) they have been assumed to bewater wet for most stimulation fluid design programs. Most slickwaterstimulation treatments were originally formulated for these tightsandstone reservoirs, and to a great extent were adapted “as is” to thegas shale market as it grew. However, due to the wide variation inmineralogy and lithology of kerogen rich shales, the variation inwetting characteristics from reservoir-to-reservoir, andformation-to-formation, has become a major issue. Some reservoirs withhigh total organic carbon (TOC) values appear to be predominantly if notcompletely oil-wet. Other shale-like formations, correctly referred toas mudstones or siltstones, appear to be of mixed wettability.Furthermore, any exploitation of the shale reserves requires injectionof large quantities of water-based fluids during hydraulic fracturingtreatments—and most of this water is not recovered.

Damage to the fracture conductivity and damage to the near-fracturematrix permeability caused by residual water is a major concern. It ishypothesized by many that fracture cleanup and the formation of waterblocks in the matrix will be determined by the extent to which thefracturing fluid wets the formation. The extent to which a fluid wetsthe surfaces of pores will determine how the fluid penetrates the porousmedium by imbibition. The extent to which a fluid wets the surface ofthe fracture face will strongly influence how effectively gas candisplace residual water in the fracture network—and may be a key factorin determining the required fracture conductivity. The contact angle isa quantitative thermodynamic measure of the relative wettability of asubstrate with respect to two fluids brought into contact with it.

There is a distinct difference between the advancing, the static and thereceding contact angles. While the advancing contact angle describes thedynamic contact angle of a fluid invading a surface, the recedingcontact angle describes the contact angle of a fluid that is displacedfrom the surface. Generally, the advancing contact angle is associatedwith imbibition, the process where a wetting fluid spontaneouslydisplaces a non-wetting fluid from a porous medium. For example,Hirasaki, G. and Zhang, D., “Surface Chemistry of Oil Recovery FromFractured, Oil-Wet Carbonate Formation”, SPE 80988 (2003) describecapillary pressure and the effects of surface chemistry on imbibitionfor oil recovery. On the other hand, the receding contact angle isassociated with drainage, the process where a wetting fluid is displacedfrom a porous medium by a non-wetting fluid. So the advancing contactangle describes the interaction between the fluid and the surface whenthe fluid flows into the rock and the receding contact angle describesthe flow of fluid out of the rock. There can be a large hysteresisbetween the two dynamic contact angles with the static contact angle,describing the angle formed by a static fluid on a surface, lyingin-between but not necessarily in the middle.

When the advancing contact angle is known, a prediction can be made asto how fast a fluid will be imbibed into a certain rock matrix or into amicrofracture. With this information, the amount of fluid that isimbibed into the rock in a given time can be calculated. The recedingcontact angle on the other hand can be used to calculate the drainage ofa wetting fluid from a rock for a given pressure applied to anon-wetting fluid. It is not only important to know how fast a fluid isimbibed into a rock, it is equally important to know how easily it comesback out. A large amount of water imbibed into the formation during atreatment may not be a problem when it is quickly driven out of the porespace after the treatment is finished. Contrary, a small amount ofimbibed fluid can cause severe water blocks if it cannot be retrievedfrom the rock matrix. The receding contact angle can also be used todetermine how quickly a treatment fluid in the fracture network isdisplaced by hydrocarbons when the well is put on production. A highreceding contact angle indicates easy displacement of the treating fluidby the hydrocarbon from the formation. In order to increase the recedingcontact angle of the treatment fluid on the fracture surface, surfaceactive additives can be used. The effectiveness of an additive can bemeasured in a drainage test with rock material that was treated with therespective additive.

Knowing the receding contact angle, treatment fluids could be designedthat contain optimum amounts of the right additive for a given rock. Forexample with hydrophilic surfaces that like to be wetted with water, anadditive that makes the surface more hydrophobic may be used so watercan be easily expelled or is not taken up in the first place.

SUMMARY

According to some embodiments, a method for determining a characteristicof an underground formation with a fluid is provided. A sample materialof the underground formation is provided. The permeability and theporosity of the sample material are measured. A drainage test isperformed on the sample material using the fluid. The threshold pressureof the sample material is estimated from the drainage test, thepermeability and the porosity measurements. The receding contact angleof the fluid on the sample material is determined from the thresholdpressure. The sample material is preferably disaggregated samplematerial. Advantageously, the disaggregation includes a grindingprocess. Advantageously, the disaggregated sample material is sieved toa specific size range.

According to some embodiments, the disaggregated material is subjectedto spinning in a centrifuge prior to the drainage test. In someembodiments, the sample material is a rock core from the undergroundformation.

Advantageously, some embodiments comprise performing an imbibition teston the sample material prior to the drainage test. The imbibition testpreferably includes an estimation of the advancing contact angle on thesample material.

Advantageously, the permeability of the sample material is measured withan inert gas at different pressures. The porosity of the sample materialcan be determined using the bulk volume and the grain density of thesample material. The fluid can be a treating fluid and the treatingfluid comprises a surfactant type and concentration selected to maximizethe receding contact angle of the fluid on the sample material.

According to some embodiments, clay-swelling or other ancillaryrock-fluid reactions of the sample material are controlled whileperforming the drainage test.

According to some embodiments, the underground formation is alow-permeability formation with a reservoir matrix permeability of lessthan 0.1 mD. The underground formation can also be a low-permeabilityformation that has a reservoir matrix permeability of less than 1 microDarcy. The underground formation might be a low-permeability formationpenetrated by a wellbore. Advantageously, the wettability of the samplematerial is deduced from the receding contact angle of the fluid on thesample material.

According to some embodiments a characteristic of an undergroundformation is determined comprising providing a sample material of theunderground formation; determining the threshold pressure of the samplematerial from a drainage test; computing the average saturation of thesample material using a measured irreducible saturation and thesaturation at the threshold pressure; determining the average thresholdpressure of the sample material from the average saturation anddetermining the threshold pressure at the irreducible saturation of theunderground formation from the average threshold pressure, the averagesaturation and the measured irreducible saturation.

According to some embodiments a method for enhancing hydrocarbonrecovery from a low-permeability formation is provided. A treating fluidis caused to contact the underground formation such that the treatingfluid is imbibed by the formation, thereby increasing hydrocarbonrecovery, wherein the treating fluid is selected based at least in parton the determination of the receding contact angle of the treating fluidon the underground formation.

According to some embodiments a formation treating fluid for enhancinghydrocarbon recovery from an underground formation is provided. Theformation treating fluid comprises at least one constituent selectedbased at least in part on a quantitative determination of thepermeability and the porosity of the underground formation and adrainage test carried out on the sample of the underground formation andthe at least one constituent. Preferably, the drainage test comprisesdetermination of the receding contact angle of the at least oneconstituent on the sample of the underground formation.

According to some embodiments it is provided a method for determiningthe effect of a fluid on a rock formation comprising determining thepermeability and the porosity of the rock formation; saturating the rockformation with the fluid; determining the threshold pressure of the rockformation imbibed with the fluid from a drainage test, the permeabilityand the porosity of the rock formation; determining a cleanup ratio ofthe fluid for the rock formation using the ratio of the thresholdpressure and the maximum threshold pressure wherein the maximumthreshold pressure is the threshold pressure for a perfectly wettingfluid; determining the effect of the fluid on the rock formation fromthe cleanup ratio. Advantageously, the receding contact angle of thefluid on the rock formation is determined from the threshold pressure.Advantageously, an imbibition test is performed on the rock formationprior to the drainage test and the imbibition test can include anestimation of the advance contact angle on the rock formation.Advantageously, the effects of a first and second fluids on the rockformation can be compared using the clean-up ratio of the first andsecond fluids respectively. Advantageously, the rock formation isdisaggregated to form a disaggregated rock formation sample and theeffect of a fluid on a rock formation are determined from thedisaggregated rock formation sample.

According to some embodiments, it is provided a method of selecting anappropriate treatment fluid for enhancing hydrocarbon recovery from anunderground formation. The porosity of a first sample material of theunderground formation is determined. The first sample material is testedfor drainage characteristics for a first candidate fluid. Thedetermination of porosity and testing drainage characteristics isrepeated for each of one or more subsequent sample materials fromunderground formation and each of one or more subsequent candidatefluids. A candidate fluid is selected based at least in part on thedrainage testing and porosity determinations, the selected candidatefluid forming at least part of the treatment fluid. Advantageously, eachtesting for drainage characteristics includes an estimation of thereceding contact angle for each sample material and candidate fluid,each estimation of receding contact angle being based in part on thedetermination of porosity of the sample material, and step of selectinga candidate fluid being based in part on the estimations of recedingcontact angle. Advantageously, the sample material comprisesdisaggregated material from the underground formation. Advantageously,the candidate fluid is imbibed in the sample material to reach completesaturation. Advantageously, an imbibition test on the sample material isperformed prior to the drainage test and the candidate fluid is selectedbased at least in part on the fact that, with the candidate fluid, thereduction of the drainage contact angle on the sample material is lessthan the reduction of the advancing contact angle on the samplematerial.

According to some embodiments, it is provided a method for determining acharacteristic of an underground formation with a fluid comprisingproviding a sample material of the underground formation; imbibing thesample material with a first imbibing fluid; performing a drainage teston the sample material imbibed with the first imbibing fluid; measuringa surface property of the sample material; repeating steps (b) to (d)for at least a second imbibing fluid; plotting the measured surfaceproperties of the sample material against each surface tension of thefirst and second imbibing fluids; comparing the resulting curve with aset of curves determined for a material with known wettability;determining the wettability of the sample material from the comparison.

As used herein the term “shale” refers to mudstones, siltstones, limeymudstones, and/or any fine grain reservoir where the matrix permeabilityis in the nanodarcy to microdarcy range.

As used herein the term “gas” means a collection of primarilyhydrocarbon molecules without a definite shape or volume that are inmore or less random motion, have relatively low density and viscosity,will expand and contract greatly with changes in temperature orpressure, and will diffuse readily, spreading apart in order tohomogeneously distribute itself throughout any container.

As used herein the term “oil” means any naturally occurring, flammableor combustible liquid found in rock formations, typically consisting ofmixture of hydrocarbons of various molecular weights plus other organiccompounds such as is defined as any hydrocarbon, including for examplepetroleum, gas, kerogen, paraffins, asphaltenes, and condensate.

As used herein the term “condensate” means a low-density mixture ofprimarily hydrocarbon liquids that are present as gaseous components inraw natural gas and condense out of the raw gas when the temperature isreduced to below the hydrocarbon dew point temperature of the raw gas.

BRIEF DESCRIPTION OF THE FIGURES

The present disclosure is further described in the detailed descriptionwhich follows, in reference to the noted plurality of drawings by way ofnon-limiting examples of exemplary embodiments, in which like referencenumerals represent similar parts throughout the several views of thedrawings, and wherein:

FIG. 1 illustrates a system for enhancing recovery of hydrocarbons froma low-permeability hydrocarbon reservoir, according to some embodiments;

FIG. 2 represents a schematic showing of the spatial relationshipsduring centrifuge test; sample length is L (cm);

FIG. 3 represents results from a typical drainage test showing howvariables are related;

FIG. 4 represents an illustration of the use of the clean-up ratio.

DETAILED DESCRIPTION

The following description provides exemplary embodiments only, and isnot intended to limit the scope, applicability, or configuration of thedisclosure. Rather, the following description of the exemplaryembodiments will provide those skilled in the art with an enablingdescription for implementing one or more exemplary embodiments. It beingunderstood that various changes may be made in the function andarrangement of elements without departing from the spirit and scope ofthe invention as set forth in the appended claims.

Specific details are given in the following description to provide athorough understanding of the embodiments. However, it will beunderstood by one of ordinary skill in the art that the embodiments maybe practiced without these specific details. For example, systems,processes, and other elements in the invention may be shown ascomponents in block diagram form in order not to obscure the embodimentsin unnecessary detail. In other instances, well-known processes,structures, and techniques may be shown without unnecessary detail inorder to avoid obscuring the embodiments. Further, like referencenumbers and designations in the various drawings indicated likeelements.

Also, it is noted that individual embodiments may be described as aprocess which is depicted as a flowchart, a flow diagram, a data flowdiagram, a structure diagram, or a block diagram. Although a flowchartmay describe the operations as a sequential process, many of theoperations can be performed in parallel or concurrently. In addition,the order of the operations may be re-arranged. A process may beterminated when its operations are completed, but could have additionalsteps not discussed or included in a figure. Furthermore, not alloperations in any particularly described process may occur in allembodiments. A process may correspond to a method, a function, aprocedure, a subroutine, a subprogram, etc. When a process correspondsto a function, its termination corresponds to a return of the functionto the calling function or the main function.

Furthermore, embodiments of the invention may be implemented, at leastin part, either manually or automatically. Manual or automaticimplementations may be executed, or at least assisted, through the useof machines, hardware, software, firmware, middleware, microcode,hardware description languages, or any combination thereof. Whenimplemented in software, firmware, middleware or microcode, the programcode or code segments to perform the necessary tasks may be stored in amachine readable medium. A processor(s) may perform the necessary tasks.

FIG. 1 illustrates a system for enhancing recovery of hydrocarbons (inthis example gas 100) from a hydrocarbon reservoir 102, according tosome embodiments. The system utilizes a borehole 103 which is formed bydrilling through various layers of rock (collectively, overburden 104),if any, to the reservoir 102. The reservoir 102 is described in oneexample as a shale reservoir. However, according to some embodimentsother types of reservoirs can benefit. For example, according to someembodiments the reservoir 102 is another type of reservoir having lowpermeability or even a conventional type of reservoir. It is alsobelieved that many of the techniques described herein can practically beapplied to any reservoirs, including those having low matrixpermeability (i.e. between 10 nanodarcies (nD) and 100 mD, where 1D=9.87×10⁻¹³ m²). According to some embodiments, the reservoir 102 isheterogeneous and/or has mixed wet characteristics.

The recovery enhancing system of FIG. 1 includes a fluid storage tank106, a pump 108, a well head 110, and a gas recovery flowline 112. Thefluid tank 106 contains a treating fluid formulated to promoteimbibition in the low permeability reservoir 102. For example, thetreating fluid may be an aqueous solution including surfactants thatresult in a surface tension adjusted to optimize imbibition based atleast in part on determination or indication of the wettability of theformation, permeability of the formation, or both. The treating fluid114 is transferred from the tank to the borehole using the pump 108,where the treating fluid comes into contact with the reservoir. Thephysical characteristics of the treating fluid facilitate migration ofthe treating fluid into the reservoir. In particular, the treating fluidenters the pore space when exposed to the reservoir, e.g., for hours,days, weeks, or longer. Entrance of the treating fluid into the porespace tends to displace gas from the pore space. The displaced gasmigrates from a portion of the reservoir 116 to the borehole 103 throughthe pore space, via the network of natural and/or induced fractures.Within the borehole, the gas moves toward the surface as a result ofdifferential pressure (lower at the surface and higher at the reservoir)and by having a lower density than the treating fluid. The gas is thenrecovered via the pipe (flowline) at the wellhead. The recovered gas isthen transferred directly off site, e.g., via flowline 112.

The receding contact angle can be used to calculate the drainage of awetting fluid from a rock for a given pressure applied to a non-wettingfluid. The receding contact angle can also be used to determine howquickly a treatment fluid in the fracture network is displaced byhydrocarbons when the well is put on production. A high receding contactangle indicates easy displacement of the treating fluid by thehydrocarbon from the formation. In order to increase the recedingcontact angle of the treatment fluid on the fracture surface, surfaceactive additives can be used. The effectiveness of an additive can bemeasured in a drainage test with rock material that was treated with therespective additive.

On the basis of this dynamic contact angle, formation treatments can beoptimized so that treatment fluids that contain optimum amounts of theright additive for a given rock are chosen. For example with hydrophilicsurfaces that like to be wetted with water, an additive that makes thesurface more hydrophobic may be used so water can be easily expelled oris not taken up in the first place. Here, we present an experimentaldrainage method to measure the saturation dependent capillary pressurein a rock sample with which a receding contact angle of a fluid on areservoir material can be estimated.

In order to measure a receding contact angle in a sample, the fluidneeds to “recede” from the sample. This can be achieved by displacingthe fluid with which the sample is saturated with another, immisciblefluid (or gas) that is pressed into the sample. The method most oftenused in a current practice is a displacement test where a treatingfluid, usually gas, is pressed through a rock material of considerablesize (about 500 g material). The pressure which is needed to press theliquid through the rock material is recorded. However, viscous fingeringand phase trapping can lead to erroneous measurement results. It mightalso be difficult to calculate a receding contact angle via this method.However, this method can be used as an “index test”—it allows theinvestigator to compare the relative effects of two fluids on the samerock, but it does not provide satisfactory quantitative fundamental datathat can be fed into a mathematical model of the system, for example.

Another method to drive a fluid out of a sample is to place the sampleinto a centrifuge. At a high enough rotational speed the fluid will flowout of the sample and is replaced—rather than displaced—by either air oranother liquid on top of the sample. This way viscous fingering andphase trapping are minimized and it has been found that the requiredamount of sample can be reduced considerably. McCollough et al (SeeMcCullough, F. W., F. W. Albaugh, and P. H. Jones, Determination ofInterstitial-Water Content of Oil and Gas Sand by Laboratory Tests ofCore Samples. Drill. & Prod. Prac. API, 1944: p. 180-188) publishedfirst centrifuge experiments on sandstone core samples in the petroleumliterature in 1944 following the work of earlier soil scientists (1907)(Briggs, L. J. and J. W. McLane, The Moisture Equivalents of Soil. Bull.No. 45, US Dept. of Agriculture, 1907: p. 5-23). They determined thesaturation of the sample by measuring the electrical conductivity.

Just one year later, in 1945, Hassler and Brunner presented a firstmathematical model, which—with refinements—is still widely used in thepetroleum industry today (Hassler, G. L. and E. Brunner, Measurement ofCapillary Pressures in Small Core Samples. Petroleum Technology, 1945.March 1945: p. 114-123). They presented a simple approximation toconvert average saturation to end-face saturation (Skuse, B., A.Firoozabadi, and H. J. Ramey. Jr., Computation and Interpretation ofCapillary Pressure From a Centrifuge. SPE Formation Evaluation, 1992.March 1992: p. 17-24). Comparison with results found by porous-platemethod showed good agreement of the drainage capillary pressure curves(Slobod, R. L., A. Chambers, and W. L. J. Prehn, Use of Centrifuge forDetermining Connate Water, Residual Oil and Capillary Pressure Curves ofSmall Core Samples. Trans. A.I.M.E, 1951. 192: p. 127-13). Manyvariations and improvements to Hassler and Brunner's method ofcalculating saturation and experimental procedure followed in the nextdecades (See Hoffman, R. N., A Technique for the Determination ofCapillary Pressure Curves Using a Constantly Accelerated Centrifuge.Trans. A.I.M.E, 1963. 228: p. 227-235 or Luffel, D. L., FurtherDiscussion of a Technique for the Determination of Capillary PressureCurves Using a Constantly Accelerated Centrifuge. SPEJ, 1964. June 1964:p. 191-192 or Szabo, M. T., New Methods for Measuring ImbibitionCapillary Pressure and Electrical Resistivity Curves by Centrifuges.SPEJ, 1974. June 1974: p. 243-252 or Firoozabadi, A., H. Soroosh, and G.H. Hasanpour, Drainage Performance and Capillary-Pressure Curves With aNew Centrifuge. JPT, 1988. July 1988: p. 913-919 and Bentsen, R. G. andJ. Anli, Using Parameter Estimation Techniques To Convert CentrifugeData Into a Capillary-Pressure Curve. SPEJ, 1977. February 1977: p.57-64). In 1986 Rajan proposed an analytical solution to the problem ofaccounting for the changing centrifugal force along the sample length(see Rajan, R. R., Theoretically Correct Analytical Solution forCalculating Capillary Pressure-Saturation from Centrifuge Experiments.SPWL Logging Symp., 1986). This solution, while computationally complex,gives an accurate saturation distribution along the length of the sampleand allows converting average saturation into inlet-face saturation.

In equilibrium the capillary pressure in a drainage experiment is equalto the average fluid pressure in a sample in the centrifuge. If thefluid pressure is higher than the capillary pressure, fluid will flowout of the sample. If the fluid pressure is equal or lower than thecapillary pressure, the fluid will remain in the sample. The centrifugalpressure, equivalent to a hydrostatic pressure, is given by:

p=ρgh  Eqn. (1)

with ρ being the density of the fluid, g being the acceleration and hbeing the rock material height. Acceleration is proportional to thedistance from the pivot-point of the centrifuge arm and will changealong the length of the sample rock material (see Kyte, J. R., ACentrifuge Method To Predict Matrix-Block Recovery in FracturedReservoirs. Society of Petroleum Engineers Journal, 1970. June: p.164-170). The mean acceleration within the sample and the sample heightare given as:

g=½ω²(r ₁ +r ₂)  Eqn. (2)

h=r ₂ −r ₁  Eqn. (3)

wherein r₁ and r₂ are the radii of rotation to the inner and the outerfaces of the sample, respectively and ω is the rotation speed of thecentrifuge.

Combining equations (1), (2) & (3) leads to an expression for thecapillary pressure in a centrifugal drainage experiment:

p _(c)=½ρω²(r ₂ ² −r ₁ ²)  Eqn. (4)

Since r₂ is fixed (see FIG. 2), the height L of the sample determinesr₁. In fact Eqn. (4) should contain the difference of the densities ofthe wetting and non-wetting fluids Δρ. The non-wetting fluid is air,whose density (ρ=0.0012 g/cm³) is so small compared to the density ofwater (ρ=1 g/cm³) that we can rightfully neglect it.

At a given angular velocity, a pressure gradient develops in the wettingfluid; the pressure drives the removal of wetting fluid from allcapillaries capable of flow at or below that pressure. By increasing therotational speed, the centrifugal pressure is increased and water isdriven out of the sample until the centrifugal pressure equals thecapillary pressure. As the pressure is increased, smaller and smallercapillaries will be drained. Since the non-wetting fluid, air in thiscase, replaces rather than displaces the imbibant, issues of viscousfingering are avoided. The mass m of the removed imbibant is determinedafter each velocity stage which is held for approximately 10 minutes toensure equilibrium is reached. The initial mass m_(f) of imbibant (indexf for fluid) is known from the imbibition experiment—it is thedifference of the mass of the sample tube before and after theimbibition: m_(f)=m_(total)−m_(dry). The water driven out of the sampleby the centrifugal pressure reduces the average saturation of the sampleand the average saturation across the sample can be computed:

$\begin{matrix}{{\overset{\_}{S}}_{w} = \frac{m_{f} - m}{m_{f}}} & {{Eqn}.\mspace{14mu} (5)}\end{matrix}$

The saturation-dependent capillary pressure p_(c) of the sample is givenas:

p _(c)(S _(w))=½Δρω²(r ₂ ² −r ₁ ²)  Eqn. (6)

where Δρ is the difference between the gravities of the wetting andnon-wetting fluids, ω is the angular velocity of the centrifuge and r₁and r₂ are the radii of rotation to the inner and the outer faces of thesample, respectively. In our measurements the rock sample is saturatedwith an aqueous fluid that is replaced by air as a non-wetting fluidduring the drainage process. The pressure in the non-wetting air is theambient pressure. The pressure in the wetting phase is actuallynegative. The method is based upon the reasonable assumption that theouter end of the rock sample remains completely saturated, and thecapillary pressure there is zero.

Hassler and Brunner suggest a simple first order correction of thecalculated saturation for the fact that the centrifugal acceleration isnot the same across the sample (Hassler, G. L. and E. Brunner,Measurement of Capillary Pressures in Small Core Samples. PetroleumTechnology, 1945. March 1945: p. 114-123).

$\begin{matrix}{{S_{w}\left( P_{c} \right)} = {{\overset{\_}{S}}_{w} + {P_{c}\frac{{\overset{\_}{S}}_{w}}{P_{c}}}}} & {{Eqn}.\mspace{20mu} (7)}\end{matrix}$

The acceleration depends on the distance of the sample from the axis ofrotation in the centrifuge. As the real sample has a definite length theacceleration at the top of the sample is different from that at thebottom of the sample. Given the fact that 65 years ago Hassler andBrunner had to hand-calculate the corrections they argued that forratios of r₁/r₂>0.7 a correction would not be necessary. In anexperimental setup this would allow uncorrected measurements for samplelengths of up to 5 cm. However, using modern computer technology it ispreferable to make the correction for smaller samples also. Our rocksample heights are usually around 3 cm.

If the diameter of the rock sample is small, one can safely ignoreradial differences in capillary pressure that occur. The radial changein the gravitational force can also be safely ignored. If the sample isshort, relative to the radius of the centrifuge arm, then one canneglect the variation in centrifugal force along the axis of thespecimen.

Rajan (Rajan, R. R., Theoretically Correct Analytical Solution forCalculating Capillary Pressure-Saturation from Centrifuge Experiments.SPWL Logging Symp., 1986) chose not to ignore the axial variation incapillary pressure, and suggested the following equation to calculatethe capillary pressure dependent saturation:

$\begin{matrix}{{S_{w}\left( P_{ci} \right)} = {{{\overset{\_}{S}}_{w}\left( P_{ci} \right)} + {\frac{2R}{1 + R}P_{ci}\frac{{{\overset{\_}{S}}_{w}\left( P_{ci} \right)}}{P_{ci}}} + {\frac{R}{1 - R^{2}}{\int_{0}^{P_{cri}}{\left\{ \frac{1 - \left\lbrack {1 - {\frac{P_{c}}{P_{ci}}\left( {1 - R^{2}} \right)}} \right\rbrack^{\frac{1}{2}}}{\left\lbrack {1 - {\frac{P_{c}}{P_{ci}}\left( {1 - R^{2}} \right)}} \right\rbrack^{\frac{1}{2}}} \right\}^{2}\frac{{{\overset{\_}{S}}_{w}\left( P_{c} \right)}}{P_{c}}\ {P_{c}}}}}}} & {{Eqn}.\mspace{14mu} (8)}\end{matrix}$

In Eqn. 8,

${R = \frac{r_{1}}{r_{2}}},$

and r₁ and r₂ represent the distances of the inlet and outlet faces ofthe sample from the axis of rotation—see FIG. 2. By eliminating thethird term in Eqn. 8 and setting R to 1, the equation proposed byHassler and Brunner is obtained; therefore, the Rajan method may be seenas a correction to the Hassler and Brunner method.

The main criticism of the Hassler and Brunner and Rajan methods is theneed to compute derivatives using the raw data and the potentially largeerrors that might result. In an embodiment of the invention, aspreadsheet and straightforward numerical techniques were used toanalyze data based upon Eqn. 8, and it shows that, when R=0.85, theRajan method reproduced a theoretical capillary pressure curve with anaverage error of slightly less than −2% compared to an error obtainedusing the Hassler and Brunner method of −13.8%.

Ayappa et al. compared three centrifuge data analysis methods andconcluded that the Rajan method was the best, especially at lower Rvalues (See Ayappa, K. G. and H. T. Davies, Capillary Pressure:Centrifuge Method Revisited. AIChE Journal, 1989. 35(3): p. 365-372).

The threshold pressure is, strictly speaking, the lowest pressurerequired to force a non-wetting fluid into a porous medium that has beencompletely saturated with a wetting fluid. If the porous medium isconsidered to be an ensemble of capillaries of varying radii, then thethreshold pressure corresponds to the pressure required to displacewetting fluid from the largest capillaries. Once the largest capillarieshave been drained, the displacement pressure must be increased beforethe next largest capillaries begin to drain, and this process can becontinued until no further increase in pressure will remove additionalwetting fluid; the saturation at this point is the irreduciblesaturation.

Estimating the Receding Contact Angle

Bear (see Bear, J., Dynamics of Fluids in Porous Media. 1972, New York:Dover Publications, Inc) states that the threshold pressure expressionfor a capillary can be adapted to a porous medium if the capillary tuberadius is replaced by some mean or equivalent diameter r*.

$\begin{matrix}{P_{t} = \frac{2{\gamma cos\theta}}{r^{*}}} & {{Eqn}.\mspace{14mu} (9)}\end{matrix}$

Note that in the equation above the argument presented by Bear has beenmade more general by not assuming perfect wetting. Based upon a modelused to describe imbibition like the one described in U.S. patentapplication Ser. No. 12/914,463, entitled “Enhancing HydrocarbonRecovery”, the equivalent diameter can be expressed as

$\begin{matrix}{r^{*} = \sqrt{\frac{8k}{\varphi^{3}}}} & {{Eqn}.\mspace{14mu} (10)}\end{matrix}$

Making the substitution:

$\begin{matrix}{P_{t} = {2\gamma \; \cos \; \theta \sqrt{\frac{\varphi^{3}}{8k}}}} & {{Eqn}.\mspace{14mu} (11)}\end{matrix}$

The equation above is correct for terms expressed in SI units. Withpermeability expressed in mD and expressing the pressure in psi, Eqn. 11takes the following form

$\begin{matrix}{P_{t} = {{4.616\left( {2{\gamma cos}\; \theta \sqrt{\frac{\varphi^{3}}{8k}}} \right)} = {3.264\gamma \; \cos \; \theta \sqrt{\frac{\varphi^{3}}{k}}}}} & {{Eqn}.\mspace{14mu} (12)}\end{matrix}$

The question of threshold pressure was investigated by Thomas, Katz andTek (Thomas, L. K., D. L. Katz, and M. R. Tek, Threshold PressurePhenomena in Porous Media. SPE Journal, 1968. June 1968: p. 174-184).The authors were interested in determining how much overpressure couldbe used in a natural gas storage system. They were able to show that thethreshold pressure could be correlated, across a broad permeabilityrange, using a simple model. Their model relates the threshold pressureto permeability, porosity, surface tension and the formation factor.Thomas et al. derived the following expression:

$\begin{matrix}{P_{t} = {\frac{0.1461\sigma}{\sqrt{k_{0}}F}\sqrt{\frac{1}{\varphi \; k_{D}}}}} & {{Eqn}.\mspace{14mu} (13)}\end{matrix}$

Like Bear, the authors assumed that their samples were perfectly wettedby water, i.e. contact angle of 0°. In the equation above, σ is thesurface tension, k₀ is a shape factor (varies from 2 to 3), k_(D) is thepermeability in Darcy and F is the formation factor.

Through the use of resistivity measurements, it has been determined thatrock samples used in applications of the method of the invention wereappropriately represented using a formation factor equal to thereciprocal of the square of the porosity (Amyx, J. W., Bass, D. M., andWhiting, R. L., Petroleum Reservoir Engineering, McGraw-Hill BookCompany, New York, N.Y. (1960) p. 115). Substituting and converting thepermeability from Darcys to mD, we obtain:

$\begin{matrix}{P_{t} = {{\frac{0.1461\sigma}{\sqrt{k_{0}}\frac{1}{\varphi^{2}}}\sqrt{\frac{1}{\varphi \; k_{D}}}} = {{\frac{0.1461\sigma}{\sqrt{k_{o}}}\sqrt{\frac{\varphi^{3}}{k_{D}}}} = {\frac{4.620\sigma}{\sqrt{k_{0}}}\sqrt{\frac{\varphi^{3}}{k}}}}}} & {{Eqn}.\mspace{14mu} (14)}\end{matrix}$

Comparing Eqn. 12 with Eqn. 14, we can determine the value of k₀required to make the two approaches equivalent when θ is 0°:

$\begin{matrix}{{3.264\gamma \; \cos \; \theta \sqrt{\frac{\varphi^{3}}{k}}} = {{3.264\gamma \sqrt{\frac{\varphi^{3}}{k}}} = {\frac{4.620\gamma}{\sqrt{k_{0}}}\sqrt{\frac{\varphi^{3}}{k}}}}} & {{Eqn}.\mspace{14mu} (15)}\end{matrix}$

Solving for k₀ yields a value of 2.01, this is within the rangespecified by Thomas et al. It appears that the model of a porous mediumdeveloped to describe imbibition into sample columns is consistent withthe model proposed by Thomas et al.

Solving Eqn. 12 for the contact angle, we obtain:

$\begin{matrix}{\theta = {\arccos\left( {\frac{P_{t}}{3.264\gamma}\sqrt{\frac{k}{\varphi^{3}}}} \right)}} & {{Eqn}.\mspace{14mu} (16)}\end{matrix}$

The equation above is correct when the threshold pressure is in psi, thepermeability is expressed in mD and the surface tension is expressed indyne/cm.

Estimating the Average Threshold Pressure

The threshold pressure is, strictly speaking, the lowest pressurerequired to force a non-wetting fluid into a porous medium that has beencompletely saturated with a wetting fluid. If the porous medium isconsidered to be an ensemble of capillaries of varying radii, then thethreshold pressure corresponds to the pressure required to displacewetting fluid from the largest capillaries. Once the largest capillarieshave been drained, the displacement pressure must be increased beforethe next largest capillaries begin to drain, and this process can becontinued until no further increase in pressure will remove additionalwetting fluid; the saturation at this point is the irreduciblesaturation.

The permeability value measured in the laboratory represents an averageof the flow through pores of varying sizes. The bundle of capillariesmodel relates the permeability to the square of the mean capillaryradius and the porosity.

We studied synthetic porous media consisting of bundles of capillarieswhose radii were geometrically and log-normally distributed. Weconcluded that the geometric mean provided a good estimate for the meancapillary radius for either geometrically or log-normally distributedradii. Since the capillary pressure varies inversely with radius, themean capillary pressure will be inversely proportional to the geometricmean of the smallest and largest radii making up the ensemble.Therefore, we used the geometric mean, P_(pro), to compute the recedingcontact angle using the permeability measured in the laboratoryaccording to

$\begin{matrix}{{\cos \; \theta_{A}} = \frac{P_{pro}\sqrt{k_{A}}}{3.264\gamma_{A}\sqrt{\varphi_{A}^{3}}}} & {{Eqn}.\mspace{14mu} (17)}\end{matrix}$

From this it can now be given steps to determine the receding contactangle of the concerned rock material.

Step 1. Estimate the threshold pressure, P_(A), (Refer to FIG. 3 for adepiction of the various parameters) from the results of a centrifugetest. The capillary pressure data for the RPM range below 1000 is fittedwith a cubic polynomial function and standard mathematical techniquesare used to calculate the inflection point which represents thethreshold pressure. P_(A) is directly related to the largest capillaryin the ensemble (See Greenkorn, R. A., Flow Phenomena in Porous Media.1983, New York: Marcel Dekker, Inc.).

Step 2. Compute the average saturation (S_(avg)) using the measuredirreducible saturation (S_(irr)) and the saturation at the thresholdpressure (S_(A)):

$\begin{matrix}{S_{avg} = {\left\lfloor \frac{S_{A} - S_{irr}}{2} \right\rfloor + S_{irr}}} & {{Eqn}.\mspace{14mu} (18)}\end{matrix}$

Step 3. Draw a vertical line (red dashed line in FIG. 3) at x=S_(avg).Note where the vertical line passes through the curve used to fit thedata, i.e. the point (S_(avg), P_(avg)).

Step 4. Connect the points (S_(A), P_(A)) and (S_(avg), P_(avg)) andextrapolate the line to intersect with the vertical line that passesthrough the irreducible saturation. The point of intersection is(S_(irr), P_(irr)). P_(irr) is associated with the radius of thesmallest capillary in the ensemble.

Step 5. The average capillary pressure lies between P_(A) and P_(irr).Earlier, we concluded that the geometric mean provides a good estimatefor the average for either geometrically or log-normally distributedpore sizes, therefore we use the geometric mean, or

P _(pro)=√{square root over (P _(A) P _(irr))}  Eqn. (19)

Comparing the Effects of Fluid Additives on Porous Materials—CleanupRatio

First, a test solution containing additive A in the baseline fluid isimbibed into the porous medium whose permeability (k_(A)) and porosity(Ø_(A)) are known. Also known, is the surface tension (γ_(A)) of thetest fluid. The saturated medium is then subjected to a drainage test,preferably centrifugation, to determine the threshold pressure (P_(A)).The contact angle is related to the known parameters via:

$\begin{matrix}{P_{A} = {3.264\gamma_{A}\cos \; \theta_{A}\sqrt{\frac{\varphi_{A}^{3}}{k_{A}}}}} & {{Eqn}.\mspace{14mu} (20)}\end{matrix}$

For the purpose of obtaining a cleanup ratio, however, we only need themeasured threshold pressure P_(A).

$\begin{matrix}{P_{A} = \frac{2\gamma_{a}\cos \; \theta_{A}}{r_{L}}} & {{Eqn}.\mspace{14mu} (21)}\end{matrix}$

We now introduce a theoretical maximum threshold pressure P_(B) ₀ whichis the threshold pressure that would result from a test using anidentical porous material as was used to determine P_(A), but if thebase fluid without additive A exhibited a surface tension of γ_(B) andthe fluid were perfectly wetting. Therefore,

$\begin{matrix}{P_{B_{0}} = \frac{2\gamma_{B}{\cos (0)}}{r_{L}}} & {{Eqn}.\mspace{14mu} (22)}\end{matrix}$

P_(B) ₀ is the threshold pressure that would result if the base fluidwithout additive A were perfectly wetting. The cleanup ratio R isintroduced as the ratio of the measured threshold pressure to themaximum threshold pressure.

$\begin{matrix}{R = \frac{P_{A}}{P_{B_{0}}}} & {{Eqn}.\mspace{14mu} (23)}\end{matrix}$

Substituting Eqn. 21 and Eqn. 22 into Eqn. 23 yields:

$\begin{matrix}{R = {\frac{\gamma_{A}}{\gamma_{B}}\cos \; \theta_{A}}} & {{Eqn}.\mspace{14mu} (24)}\end{matrix}$

Substituting Eqns. 17 and 19 for cos θ_(A) yields:

$\begin{matrix}{R = {{\frac{\gamma_{A}}{\gamma_{B}}\frac{\sqrt{P_{A}P_{irr}k_{A}}}{3.264\gamma_{A}\sqrt{\varphi_{A}^{3}}}} = \frac{\sqrt{P_{A}P_{irr}k_{A}}}{3.264\gamma_{B}\sqrt{\varphi_{A}^{3}}}}} & {{Eqn}.\mspace{14mu} (25)}\end{matrix}$

Eqn. 25 can be used to evaluate the effect of an additive on cleanup.This provides a significantly superior alternative to the knownCapillary Suction Time (CST) test which is the de facto standard.

In order to assess the error associated with the cleanup ratio, wesimply use Eqn. 24 to show:

$\begin{matrix}{{dR} = {{{\frac{\cos \; \theta_{A}}{\gamma_{B}}}d\; \gamma_{A}} + {{{- \frac{\gamma_{A}\cos \; \theta_{A}}{\gamma_{B}^{2}}}}d\; \gamma_{B}} + {{{- \frac{\gamma_{A}\sin \; \theta_{A}}{\gamma_{B}}}}d\; \theta_{A}}}} & {{Eqn}.\mspace{14mu} (26)}\end{matrix}$

As the receding contact angle approaches zero, the error, dθ_(A),associated with the method used to estimate contact angle issignificant, but when the contact angle is 0, the third term vanishes,making the overall error quite small, since the surface tension valuesare known with very good accuracy.

Testing performed on rock material particles provides good results. Wehave established that rock samples formed with 140- to 200-meshparticles provide reproducible results.

Description of the Drainage Cell:

A known in the art test cell can be used to perform the drainage test.Advantageously, the tube material of the cell may comprise borosilicateglass, present low expansion, a diameter of approximately 12 mm±0.2 mmand wall thickness of approximately 1 mm±0.04 mm. A frit is attached toretain the fine, loose sample material. Advantageously, the fritcomprises borosilicate glass, has low expansion; has a diameter of 10 mmOD; a thickness of 2.5-2.6 mm; and the pore size is approximately 40-60micron. The top of the cell may have a thread assembly for attaching toa permeameter. For example the thread size can be: Ace #11, ⅝″ OD, 7threads per inch, root diameter of 0.541″.

Preparation of the Sample:

Generally in hydrocarbon recovery from subterranean formations, samplematerial from a reservoir formation is scarce. Therefore, analysistechniques that make use of only small samples is advantageous.According to some embodiments, sample sizes on the order of 5 g or lesshave been found to be sufficient. According to some embodiments, ameasurement is made using disaggregated material, and it is understoodthat grinding of the sample exposes sufficient fresh surface area so asto ensuring that the test fluid is exposed to a surface veryrepresentative of that found in the undisturbed reservoir.

The use of disaggregated material is not new and the method is known tobe used to evaluate the properties of extremely low permeabilitymaterials. For example, see: Schettler, P. D., Parmely, C. R., Lee, W.J., “Gas Storage and Transport in Devonian Shales” SPE FormationEvaluation, September 1989; Schettler, P. D., Parmely, C. R.,“Contributions to Total Storage Capacity in Devonian Shales”, SPE 23422(1991); and Luffel, D. L., Hopkins, C. W., Schettler, P. D., “MatrixPermeability of Gas Productive Shales”, SPE 26633 (1993).

Properties that can be measured using disaggregated material includepermeability, porosity, and adsorption characteristics. As an example,disaggregation provides a way to determine the matrix permeability ofhighly fractured samples. Shales often exhibit natural fractures—even onthe scale of laboratory samples. It has been found that the use ofdisaggregated materials provides a logical means to isolate the matrixpermeability.

It is believed that the grinding of the core has minimal impact on thesurface properties of the material. While the process of grinding altersthe reservoir material physically, the fresh surfaces that result fromgrinding are believed to be quite representative of the chemical natureof the surfaces of the fractured formation in its natural state.Furthermore, the surfaces of samples shaped by drilling or sawing usingeither oil or water lubricants do not accurately reflect in-situproperties.

In a preferred example of the method of the invention, a sample isground using a mixer/mill. The resulting material is dry sieved and theapproximately 140/200 mesh size material fraction is retained for themeasurement. This mesh size gives a fine powder. It should be noted,however, that this sieved material can contain aggregates of fines. Thesample is then dried to constant weight; ideally the drying temperaturewill not exceed the static temperature of the underground formation thatthe sample is coming from.

A fixed amount of the disaggregated, sieved and dried material areweighed and transferred to a sample tube which has a frit at the bottomend. The sample is then compacted by, for example, tapping the tube onthe work bench until a constant column height is achieved. Once constantheight has been achieved, the sample is transferred to a centrifuge andcan be subjected to the fastest spinning rate (for example atapproximately 5000 rpm) for about ten minutes, which enhance mechanicalstability of the material.

Measuring the Permeability of the Sample:

The gas permeability (k) of the sample rock material (in the presentexample, packed disaggregated material) is measured with a permeameterset-up with nitrogen using at least three different pressures. Forexample, the gas permeameter consists of a mass flow meter, a mass flowcontroller and a pressure gauge enabling the measurement of lowdifferential pressures (for example, Δp=1-4 psi) of a nitrogen flow (forexample, q=0.6-3 ^(cc)/_(min)) through the sample rock material. Giventhe low test pressures, the appropriate form of Darcy's Law is used tocompute the permeability. Klinkenberg effects were shown to benegligible due to the relatively high permeability of a typicalsample—such would not be the case were ultra-low permeability rocksample plugs used.

Determining the Porosity of the Sample:

The bulk volume of the disaggregated rock sample after tapping andcentrifugation is simply determined once the length and diameter of thesample are known. The absolute volume of the sample material isdetermined by dividing the mass of the sample material by the graindensity of the sample material as determined using a pycnometer. Theporosity of the sample is finally determined by dividing the differencebetween the bulk volume and the absolute volume by the bulk volume.

Performing the Drainage Test:

The drainage test is preferably performed after an imbibition test witha fully saturated sample (as described, for example in U.S. patentapplication Ser. No. 12/914,463, entitled “Enhancing HydrocarbonRecovery”). To conduct the imbibition step, the filled sample tube islowered into a reservoir of imbibant until the frit is completelyimmersed into the test liquid. When the fluid level in the columnreaches the top of the sample the imbibition is complete. The weights ofthe sample tube and the sample material before and after imbibition arerecorded. The mass change is equal to the total mass of the imbibedfluid.

The test cell with the saturated sample is then placed into a speciallyconstructed centrifuge adaptor. The adaptor contains a small glass vialat the bottom that receives the drained fluid. The level of the drainedfluid is lower than the frit of the sample tube, so that the drainedliquid cannot be re-imbibed after slowing or stopping the rotation.

After a sample has been saturated by imbibition, the sample is spun at agiven speed, for example starting at 300 rpm and increasing in 100 rpmsteps until 2000 rpm. Above 2000 rpm the angular speed might beincreased in 500 rpm steps up to 5000 rpm. Advantageously, therespective speed is held for at least ten minutes to ensure thatequilibrium between centrifugal force and capillary pressure is reachedand no more fluid is driven out of the sample.

The fluid that is driven out of the sample tube is collected in areceptacle below the tube so that it does not contact the bottom end ofthe shale sample and, therefore, cannot be imbibed back into the sampleonce the centrifuge is stopped.

The amount of fluid collected in the receptacle serves as a confirmationof the amount of fluid drained. The effluent can be used for furtheranalysis, e.g. additive retention studies.

After stopping the centrifuge, the mass of the sample tube is recordedand the tube reinserted into the centrifuge sample holder and theprocess repeated for the next rotational speed step. Redistribution offluid during the slowdown of the rotor and the weighing process is soslow that it will not change the saturation profile appreciably, butcare should be taken to complete these steps as quickly as possible. Therotational speed which can be achieved with the used centrifuge is about5000 rpm. With this speed, centrifugal pressures of about 160 psi can beapplied to the sample.

When the last data point at 5000 RPM is collected, the average watersaturation for the respective rotational speed and the correspondingcapillary pressure (=centrifugal pressure) are calculated. In anotherembodiment, the method described here might also be implemented on coreplugs. Special adapters for core plugs have been designed and these arealso fitted with a receptacle to collect the effluent.

Results

In one implementation of a method of the invention, the rock sampleswere shale samples from three different formations—α, β and γ. Thesesamples were saturated with fluids containing various additives. Anadvancing contact angle θ_(a) was determined. The fully saturatedsamples were placed in the centrifuge and spun out. Receding contactangles δ_(r) were calculated as detailed above from the resulting data.The comparison of the measured advancing (Θ_(a)) and receding (Θ_(r))contact angles is shown in Table 1 below.

Experimental Contact Angle Formation Fluid Θ_(a) [°] Θ_(r) [°] ΔΘ [°] αKCl 77 ± 5 58 ± 7  −19 A  55 ± 14 0 ± 0 −55 B  58 ± 13 27 ± 19 −31 C  52± 16 0 ± 0 −52 D  48 ± 18 0 ± 0 −48 E  52 ± 16 0 ± 0 −52 β KCl 81 ± 3 46± 12 −35 A 65 ± 8  4 ± 164 −60 B 72 ± 6 0 ± 0 −72 C 66 ± 7 0 ± 0 −66 D66 ± 8 0 ± 0 −66 E 67 ± 7 0 ± 0 −67 γ KCl 81 ± 3 61 ± 1  −19 A 64 ± 9 56± 2  −8 B 68 ± 7 20 ± 4  −48 C 66 ± 8 33 ± 4  −33 D 64 ± 8 38 ± 3  −26 E 59 ± 11 55 ± 2  −5

In all cases the receding contact angle is smaller than the advancingcontact angle, as expected. The difference between the two dynamiccontact angles ranges between 5° and 72°. In all the tests the advancingcontact angles for the surfactant solutions were smaller than for thebrine due to the decrease in surface tension of the respective liquidscompared to brine.

When testing clearly hydrophobic rock samples (rocks from α and β) thesurfactants changed the surface properties of the shale and recedingcontact angles of zero can be measured in most of the tests. However, inrock sample of mixed wettability (γ sample), the surfactants have amixed impact on the surface characteristics.

Evaluating the Effect of Additives

As previously detailed above, one embodiment of the method of theinvention provides a means to determine the receding contact angle andwith that, the wetting characteristic of rock samples. It can also beused to compare the effect of additives on the rock itself. The clean-upratio provides a comparison between various additives with respect totheir performance on a specific rock material. The clean-up ratio,therefore, provides a means with which to optimize the design oftreatments.

FIG. 4 shows a comparison of clean-up ratios determined using fivesurfactant solutions and a brine solution and three formation samples.For the γ sample all the surfactants lower the clean-up ratio comparedto a brine. However, surfactants E and A are markedly “better”, meaningthese additives displayed a lower clean-up ratio, compared to currentsurfactants B, C and D. This shows that improvements over currentproducts are possible. The results for the reservoirs α and β show adifferent picture. Not all the surfactants decrease the clean ratiocompared to a brine and it becomes important to choose the rightsurfactant for the job. In some cases the surfactants have too littleimpact on the threshold pressure to justify their cost. It is clear thatsurfactants react differently with various rocks. Additive E, forexample, shows huge performance differences between the threeformations.

When the saturation and drainage measurement is performed with a seriesof imbibant mixtures (e.g. water/methanol mixtures with varying mixingratios) that have different surface tensions, a plot of a measuredsurface property, e.g. saturation, wetted surface area, surface energyetc, vs. surface tension can be composed. The resulting curve will havea characteristic shape depending on the wettability of the sample. Acomparison with a set of curves determined for material with knownwettability allows a qualitative deduction of the wettability of themeasured material.

Additive and Fluid Evaluation

In addition to a need for determining the contact angle of the nativerock with a brine, pure water or other simple fluid, the industry needsquantitative test methods for determining how various chemical additivesto a treatment fluid can change the wetting characteristics, orcapillary pressures within a subterranean rock. To address this need themethod proposes embodiments to test how surface active agents(surfactants, water soluble polymers and clay stabilizers) can changethe wetting condition on the surface of the rock while otherphysical/chemical processes are taking place in these complex rocks.Fluid and additives can do things other than modify the drainage contactangle. Additives can impact the magnitude of clay swelling in the rock,chemical weathering of the rock, and modify the native salt environmentin the rock. All of these issues can lead to erroneous results andinterpretations if not addressed or by applying the drainage analysiswithout thought. One embodiment of the method of the invention isdesigned so that each of these factors could be dealt with in turn,which leads to a number of examples highlighted below.

Native shales and mudstones often contain swelling clays (smectite andmontmorillonite being examples), and as such the texture,three-dimensional structure and pore network of these rocks can bechanged by exposure to fluids (particularly water). Also these rocks canbe cemented together by soluble or partially soluble cementation agents(calcium carbonate, gypsum being examples). These changes to the rockand pore structure occur independently of the wetting behavior of theadvancing fluid. This is true both for porous rock, and for granulatedsamples made of these rocks. This effect can complicate theinterpretation of centrifuge-drainage experiments because theseexperiments assume that the pore structure stays constant for theduration of the experiment.

One embodiment of our invention uses knowledge of the rock, and theselective use of clay stabilizing ions to minimize this complication.Since surface tension γ is measured independently before the test, wecan factor out the impact of the clay stabilizer on our calculated valuefor θ. Since k, and φ are independently measured for each test prior tothe experiment, and since we can measure k after the experiment aswell—we can detect structural changes to the matrix.

Another embodiment includes pretreatment of the surfaces of granularmaterial to assist in the differentiation of wetting affects (on thesurface of the rock) and the reduction in interfacial fluid tension(between the two mobile phases). That is so that we can distinguishbetween θ and γ in equation 4. Pre-treatment of the sample can also beused to minimize the development of concentration gradients of surfaceactive species in the rock sample. Additives that are highly adsorptionprone will likely not move at the same velocity through the sample asthe wetting fluid. It is also possible to analyze the effluent by takingsamples after each stage of the drainage test.

In addition to changing the contact angle of surfaces we know thatvarious additives such as polyacrylamides or polysulphonates cansignificantly change the permeability and porosity of samples ofmaterial due to their ability to instigate agglomeration or dispersionof fine particulate material. As such, the “comparative Washburn” methoddescribed above would not work. The proposed method of independentlymeasuring permeability k and porosity φ is preferable in order to makethe pre-treatment embodiment work and to distinguish wetting effectsfrom other effects.

In the drainage method described in this memo, the sample of granularmaterial is prepared as described above. The permeability k and porosityφ of the sample is then measured. The permeability is measured withrespect to a non-wetting gas. The test fluid is then imbibed into thesample. This method alone could leave significant concentrationgradients in the sample—especially of surface active species such aspolyacrylamides. Therefore, in one embodiment of the invention, amplevolume of test fluid (containing the surface active species) is placedon the top of the already saturated rock sample. This fluid is thencentrifuged through the sample—treating the surface of the grains priorto the actual drainage experiment. Furthermore, the permeability of thesample to the wetting fluid can be measured during this stage as well.

Another embodiment of this method is that the test fluid and granularrock material could be slurried, and placed into the test cell as aslurry. The sample could then be centrifuged to remove excess fluid.Additional fluid could then be added to the top of the sample and awetting-fluid saturated permeability test could be run to determine k.

Numerous shale and mudstone formations contain liquid hydrocarbons aswell as gas. The imbibition test can be run against a constant orvariable head.

Another embodiment comprises the determination of the contact angle withrespect to a fluid which has a salt concentration(s) that mimics theconnate water (or of the connate water diluted by treatment fluid) ofthe formation.

Advantage of the method of the invention is also that it is designed tobe pragmatic—for high-throughput, rapid, atmospheric pressure testing offluids/rocks.

While the invention is described through the above exemplaryembodiments, it will be understood by those of ordinary skill in the artthat modification to and variation of the illustrated embodiments may bemade without departing from the inventive concepts herein disclosed.Moreover, while the preferred embodiments are described in connectionwith various illustrative structures, one skilled in the art willrecognize that the system may be embodied using a variety of specificstructures. Accordingly, the invention should not be viewed as limitedexcept by the scope and spirit of the appended claims.

1-18. (canceled)
 19. A method for determining a characteristic of anunderground formation comprising: a. providing a sample material of theunderground formation; b. determining the threshold pressure of thesample material from a drainage test; c. computing the averagesaturation of the sample material using a measured irreduciblesaturation and the saturation at the threshold pressure; d. determiningthe average threshold pressure of the sample material from the averagesaturation; e. determining the threshold pressure at the irreduciblesaturation of the underground formation from the average thresholdpressure, the average saturation and the measured irreduciblesaturation.
 20. A method for enhancing hydrocarbon recovery from alow-permeability formation comprising: causing at least one treatingfluid to contact the underground formation such that the at least onetreating fluid is imbibed by the formation, thereby increasinghydrocarbon recovery, wherein the at least one treating fluid isselected based at least in part on the determination of the recedingcontact angle of the treating fluid on the underground formation.
 21. Aformation treating fluid for enhancing hydrocarbon recovery from anunderground formation comprising at least one constituent selected basedat least in part on a quantitative determination of the permeability andthe porosity of the underground formation and a drainage test carriedout on the sample of the underground formation and the at least oneconstituent.
 22. A formation treating fluid according to claim 21,wherein the drainage test comprises determination of the recedingcontact angle of the at least one constituent on the sample of theunderground formation.
 23. A formation treating fluid according to claim21, wherein the sample of the underground formation comprisesdisaggregated material.
 24. A method for determining the effect of afluid on a rock formation comprising: a. determining the permeabilityand the porosity of the rock formation; b. saturating the rock formationwith the fluid; c. determining the threshold pressure of the rockformation imbibed with the fluid from a drainage test, the permeabilityand the porosity of the rock formation; d. determining a cleanup ratioof the fluid for the rock formation using the ratio of the thresholdpressure and the maximum threshold pressure wherein the maximumthreshold pressure is the threshold pressure for a perfectly wettingfluid. e. determining the effect of the fluid on the rock formation fromthe cleanup ratio.
 25. A method according to claim 24, furthercomprising determining the receding contact angle of the fluid on therock formation from the threshold pressure.
 26. A method according toclaim 24, further comprising performing an imbibition test on the rockformation prior to the drainage test.
 27. A method according to claim26, wherein the imbibition test includes an estimation of the advancingcontact angle on the rock formation.
 28. A method according to claim 24,further comprising repeating steps (a) to (e) for at least a secondfluid and comparing the effect of first and second fluids on the rockformation using the clean-up ratio of the first and second fluidsrespectively.
 29. A method according to claim 24, further comprising thestep of disaggregating the rock formation to form a disaggregated rockformation sample and performing steps (a) to (e) on the disaggregatedrock formation sample.
 30. A method of selecting a treatment fluid forenhancing hydrocarbon recovery from an underground formation, the methodcomprising: a. determining permeability and porosity of a first samplematerial of the underground formation; b. imbibing the first samplematerial with a first candidate fluid; c. testing the first samplematerial for drainage characteristics for the first candidate fluid; d.repeating the determining of permeability and porosity and testingdrainage characteristics for each of one or more subsequent samplematerials from underground formation and each of one or more subsequentcandidate fluids; and e. selecting a candidate fluid based at least inpart on the drainage testing, the selected candidate fluid forming atleast part of the treatment fluid.
 31. A method according to claim 30wherein each testing for drainage characteristics includes an estimationof the receding contact angle for each sample material and candidatefluid, each estimation of receding contact angle being based in part onthe determination of permeability and porosity of the sample material,and step of selecting a candidate fluid being based in part on theestimations of receding contact angle.
 32. A method according to claim30, wherein the sample material comprises disaggregated material fromthe underground formation.
 33. A method according to claim 30, whereinthe candidate fluid is imbibed in the sample material to reach completesaturation.
 34. A method according to claim 30, further comprisingperforming an imbibition test on the sample material prior to thedrainage test.
 35. A method according to claim 34, further comprisingselecting a candidate fluid based at least in part on the fact that,with the candidate fluid, the reduction of the drainage contact angle onthe sample material is less than the reduction of the advancing contactangle on the sample material. 36-37. (canceled)